The degree to which two probability distributions may be distinguished from one another in some fixed set of measurements induces a natural notion of distance on the state space [1]}.
This notion of distance and the geometrical structure it gives rise to is sometimes termed information geometry, with distinguishability being quantified by the Fisher information matrix,
\(F_{\mu \nu } \lbrace p(x|\lambda )\rbrace  = \int \frac{1}{p} {p}{\lambda _\mu }{p}{\lambda _\nu } x,\) 
